Statistical Science

Poisson Approximation and the Chen-Stein Method

Richard Arratia, Larry Goldstein, and Louis Gordon

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Abstract

The Chen-Stein method of Poisson approximation is a powerful tool for computing an error bound when approximating probabilities using the Poisson distribution. In many cases, this bound may be given in terms of first and second moments alone. We present a background of the method and state some fundamental Poisson approximation theorems. The body of this paper is an illustration, through varied examples, of the wide applicability and utility of the Chen-Stein method. These examples include birthday coincidences, head runs in coin tosses, random graphs, maxima of normal variates and random permutations and mappings. We conclude with an application to molecular biology. The variety of examples presented here does not exhaust the range of possible applications of the Chen-Stein method.

Article information

Source
Statist. Sci. Volume 5, Number 4 (1990), 403-424.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.ss/1177012015

Digital Object Identifier
doi:10.1214/ss/1177012015

Mathematical Reviews number (MathSciNet)
MR1092983

Zentralblatt MATH identifier
0955.62542

JSTOR
links.jstor.org

Keywords
Poisson approximation invariance principle Stein's method

Citation

Arratia, Richard; Goldstein, Larry; Gordon, Louis. Poisson Approximation and the Chen-Stein Method. Statist. Sci. 5 (1990), no. 4, 403--424. doi:10.1214/ss/1177012015. http://projecteuclid.org/euclid.ss/1177012015.


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See also

  • See Comment: J. Michael Steele. [Poisson Approximation and the Chen-Stein Method]: Comment. Statist. Sci., Volume 5, Number 4 (1990), 424--425.
  • See Comment: A. D. Barbour. [Poisson Approximation and the Chen-Stein Method]: Comment. Statist. Sci., Volume 5, Number 4 (1990), 425--427.
  • See Comment: Michael S. Waterman. [Poisson Approximation and the Chen-Stein Method]: Comment. Statist. Sci., Volume 5, Number 4 (1990), 427--429.
  • See Comment: Louis H. Y. Chen. [Poisson Approximation and the Chen-Stein Method]: Comment. Statist. Sci., Volume 5, Number 4 (1990), 429--432.
  • See Comment: Richard Arratia, Larry Goldstein, Louis Gordon. [Poisson Approximation and the Chen-Stein Method]: Rejoinder. Statist. Sci., Volume 5, Number 4 (1990), 432--434.